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I have been lurking here for awhile and coincidentally found this post in a google search of "Braid White Temperament."

Originally Posted By: UnrightTooner

For those that do not know, Dr. William Braid White's temperament sequence for ET is:

tune C5 to forkC4 to C5F3 to C4G3 to C4D4 to G3A3 to D4E4 to A3B3 to E4F#3 to B3C#4 to F#3G#3 to C#4D#4 to G#3A#3 to D#4F4 to A#3

I am learning to set temperaments by ear and want a basic one that uses 4ths and 5ths. Most of the beginner temperaments I am trying pivot around 3rd's which is great, but I don't hear them (or like them) as well as I do 4ths and 5ths. With the 3rds I feel like I am guessing, whereas the 4ths and 5ths are much clearer to me.

I think this temperament would be a good one for me to learn, however I have an A fork, and when transposing the sequence down a -3rd, doesn't it get a bit low?

Does anyone have a favourite temperament sequence involving mostly 4ths and 5ths that they would be willing to divulge?

I use some of the Brad White sequences in a Both-ways-from-the-Middle sort of temperament, but lately have experimented with the Marpurg sequence demonstrated by Bill Bremmer Videos The first two will apply to what you are working on, and they use 4th and 5th intervals after the contiguous 3rds exercise.

I think it has had a remarkable effect on my temperament setting. I get fewer errors and spend less time fussing. (Your mileage may vary.)

tune C4 to a C5 forkF3 to C4F4 to C4 and F3A#3 to F3 and F4G3 to C4G4 to C4 and G3D4 to G3 and G4A3 to D4E4 to A3B3 to E4F#3 to B3F#4 to B3 and F#3C#4 to F#3 and F#4 G#3 to C#4D#4 to G#3A#3 to D#4 (A#3 was already tuned)F4 to A#3 (F4 was already tuned)

There is no need to go into the detail that is already available in Dr. Whiteâ€™s book. I will explain the reasons for the changes I made, though.

There is much criticism of Dr. Whiteâ€™s method because errors can accumulate and not be noticed until later in the sequence. For me this is the value of the 4ths and 5ths method. By letting errors accumulate, they can be noticed when otherwise they would be overlooked. But by including A#3 early in the sequence, the errors can be corrected more from the ends toward C rather than more from C to one end.

On smaller pianos the 4ths and 5ths at the beginning that tune F3 and G3 can be difficult to get right because of scaling issues. This can be when there are wound strings to deal with and also when there are not. By including F4 and G4 at the beginning, a better place for F3 and G3 can be determined.

The additional notes that are above the 13 notes in Dr. Whiteâ€™s sequence, namely F#4 and G4, allow checks with M3s (major thirds) and M6s (major sixths) that would otherwise not be available. The first one that is available is the M6 A#3-G4. This will be the first RBI (rapid beating interval) available for a check and will always be above any serious scaling issues. This will also beat at the same speed as the M3 C4-E4 tuned later giving the first M6 outside M3 inside check. Again this check will be above any scaling issues, and just as important, includes the only true â€śanchorâ€ť - C4.

The most critical note is F# because it is half way around the circle of 5ths from C, and checking it to C requires a number of separate checks strung together. As mentioned before, F#4 is included to give additional checks and to help determine F#3 when there are scaling issues. And by including A#3 early in the sequence the first ladder of M3s (F#3, A#3, D4, F#4) is formed when F#3 and F#4 are tuned to tie all the needed checks together. And on top of that it will help decide just what to do with any jumps in scaling due to wound strings by providing some chromatic M3s at the bottom of the temperament octave. It is usually best to have the highest M3 that spans the wound/unwound break to beat the same speed or faster than the next M3 up. Others will disagree, but when you decide that you want the best sounding 4ths and 5ths that is what is needed.

_________________________
Jeff DeutschlePart-Time TunerWho taught the first chicken how to peck?

If you prefer a 4ths & 5ths temperament sequence, that is fine; many people do. However, if what you are trying to tune is Equal Temperament (ET), the results may be something other than what you believe you are doing and intend to do. I don't believe any human being alive can really tune ET by only using 4ths & 5ths without also checking and correcting the results with the Rapidly Beating Interval (RBI) checks.

You have already said that you don't hear them well and you feel that you are just guessing. I don't wish to appear harsh in saying this but when you estimate your way through an entire sequence using only 4ths & 5ths (with no RBI checks), you are really just guessing too!

You need to expand your listening and control ability beyond just the Slowly Beating Intervals (SBI) to include the many RBI checks that are available. Some books on the subject suggest that the SBIs represent the "coarse" adjustments and the RBIs represent the "fine" adjustments. When listening to the RBIs, it will always be a matter of comparing very small differences. No two will sound exactly alike with the exception of one test which is a favorite of many tuners: the "inside third, outside sixth" test.

If there is any participant on here who can carefully and explicitly help you learn how to use these tests, it is Tooner (Jeff D.). I wish you good luck in learning to tune aurally!

When I read in TeaGirlâ€™s OP â€ť Most of the beginner temperaments I am trying pivot around 3rd's which is great, but I don't hear them (or like them) as well as I do 4ths and 5ths. With the 3rds I feel like I am guessing, whereas the 4ths and 5ths are much clearer to me.â€ť I could connect with what I perceive when tuning CM3s, also. And I do think that she was referring to CM3s because of the use of the word "pivot". It really isnâ€™t difficult to tune a progressive set of CM3s, but I do feel like I am guessing when I do so. There is a fairly wide window of where a particular note can be placed and still have progressive CM3s. But change a 4th or 5th just Â˝ cent and you can hear a difference, that is, if you can hear the tempering of 4ths and 5ths.

But why are you injecting the idea of tuning 4ths and 5ths without RBI checks? That is the same old straw man you build just to knock down.

_________________________
Jeff DeutschlePart-Time TunerWho taught the first chicken how to peck?

It was until RBIs were introduced in the tuning sequences that true ET was achieved in the begining of XXth Century. Before that, on XIXth Century, only "Quasi ET" and "Well Temperaments" were tuned in pianos. The tuners of the time used to believe it was ET but it was not.

You can tune really nice and good sounding Well Temperaments with 4ths/5ths sequences. In fact I prefer these temperaments to the colourless ET, but to tune real ET you need RBIs, as checks or as tuning intervals, as you wish. If you can not hear them you can not tune real ET.

I will try Loren's at the moment, since I have an A fork, thanks Loren!

In the future when I try the Braid White, is it possible from an A fork or does the transposition make it too low?

In the meantime I will order a C fork...

There is a section in Dr. White's book about using the same sequence transposed down a minor third. If you have a large piano, and D3 is not on the bass bridge, there should not be a problem. But even so, if you can recognise the jump in scaling and allow the RBIs to jump in thier progression it can be done. It's just a tough way to start. But it may work for you better anyway. If the M3s are a little too fast for you, they will be a little slower starting with A.

_________________________
Jeff DeutschlePart-Time TunerWho taught the first chicken how to peck?

I guess it is a good thing that Tea Girl just prefers 4ths and 5ths and hears them better than RBIs, not that she cannot hear RBIs as you and Bill want to think. If you heard 4ths and 5ths well, you may have become a 4ths and 5ths tuner, too.

How does this sound: Unless you can hear 4ths and 5ths well, and understand what the beat speed of RBIs mean, you cannot tune true ET, only a quasi-ET. This would be apparent if the outside M6 inside M3 test was properly used.

_________________________
Jeff DeutschlePart-Time TunerWho taught the first chicken how to peck?

I guess it is a good thing that Tea Girl just prefers 4ths and 5ths and hears them better than RBIs, not that she cannot hear RBIs as you and Bill want to think.

UnrightTooner,

Are you reading?

Originally Posted By: Tea Girl

I am learning to set temperaments by ear and want a basic one that uses 4ths and 5ths. Most of the beginner temperaments I am trying pivot around 3rd's which is great, but I don't hear them (or like them) as well as I do 4ths and 5ths. With the 3rds I feel like I am guessing, whereas the 4ths and 5ths are much clearer to me.

I don't believe it to be a good thing if a tuner doesn't want or doesn't like to hear 3rds, or prefer 4ths/5ths over 3rds. The tuner has to hear/tune/test 3rds!

Originally Posted By: UnrightTooner

How does this sound: Unless you can hear 4ths and 5ths well, and understand what the beat speed of RBIs mean, you cannot tune true ET, only a quasi-ET. This would be apparent if the outside M6 inside M3 test was properly used.

This sounds perfectly correct!

You can not tune ET by merely tuning progressive 3rds, you need 4ths/5ths! To tune ET you need all of them, SBIs and RBIs.

Though, one doesn't have to use the M6 inside M3 test as an obliged way to achieve true ET. In fact I never use it because it is not a theoretically correct test: M6 inside M3 is a "quasi equal beating" test. When it sounds good you know you are on the right way, but when it sounds wrong it gives you no direct clue about the culprit(s). There are better tests available, which identify directly the wrong notes, telling you at once if they are sharp or flat and by how much.

There is one thing that the outside M6 inside M3 test has that no others have. An aug4 interval. It can check halfway around the circle of fifths. And yes, it does not point out one particular note being wrong. A number of notes may be wrong, and it may not be apparent with individual checks.

_________________________
Jeff DeutschlePart-Time TunerWho taught the first chicken how to peck?

Why start with a C fork and hope A4 ends up at 440 when that A is the critical standard? Why not set A at 440 and temper from there? I'll never figure that one out.

I have wondered the same thing and have tried some different theoretical sequences. But considering that very few pianos have F3 on the bass bridge, but many have E3 on the bass bridge, F3-F4 seems the best temperament octave. This means that either A#3 or C4 would be the best place to start so that SBIs can be used to define the temperament octave. Of the two, C4 is the obvious choice, unless perhaps you want to tip your hat to John Phillips Souza! Iâ€™d rather tip my hat to Dr. White and use a C-fork. Besides, the temperature and humidity of the room will change where A4 ends up much more than starting on C will, unless you do not tune ET.

_________________________
Jeff DeutschlePart-Time TunerWho taught the first chicken how to peck?

I guess it is a good thing that Tea Girl just prefers 4ths and 5ths and hears them better than RBIs, not that she cannot hear RBIs

I don't intend to not hear 3rds well forever... haha

It's just that the sequences I have (from the Potter course) involve tuning A4-A3, then immediately A3-F3, then usually a C# gets involved.. when I can't hear the 3rds as well as 4ths, to build the temperament off the 3rds made no sense to me. I knew there was another way and then Dan mentioned the Braid White sequence so I was looking for input!

And to space out a bit.. I just plain love the sounds of 4ths and 5ths. I love playing them and listening to them and trying to get them just so. Maybe it's a result of a Jazz background but they make me happy.

Originally Posted By: Silverwood Pianos

Tea Girl!Thatâ€™s funnyâ€¦you are still doing that high tea gig? Leigh and I will drop by when we are over there.Should be around Easter or soâ€¦â€¦

Too bad you did not ask me about this at the seminar..

Please do drop by high tea! Maybe I can treat you and Leigh, as a thank-you for your seminar.

I must admit, temperament tuning was not on my brain last weekend, it (my brain) was filled with hide glue and felts! There was just so much information there that I have about 6 pages of typewritten notes! It wasn't until I came home and spent 2 days practicing that I came to the conclusion of what might work best for me. I still have a whole list of questions that I haven't asked yet. There is just so much to learn.

Why start with a C fork and hope A4 ends up at 440 when that A is the critical standard? Why not set A at 440 and temper from there? I'll never figure that one out.

I have wondered the same thing and have tried some different theoretical sequences. But considering that very few pianos have F3 on the bass bridge, but many have E3 on the bass bridge, F3-F4 seems the best temperament octave. This means that either A#3 or C4 would be the best place to start so that SBIs can be used to define the temperament octave. Of the two, C4 is the obvious choice, unless perhaps you want to tip your hat to John Phillips Souza! Iâ€™d rather tip my hat to Dr. White and use a C-fork. Besides, the temperature and humidity of the room will change where A4 ends up much more than starting on C will, unless you do not tune ET.

I probably didn't explain right. My temperament octave IS F3-F4. But I start from an A4 reference. A4 to the fork, A3 to A4, and then a 4th's-5th's as stated above starting with A3, with the final note being D4 to G3. I then test that D against A4.

Here you first set the tempering of M3s and then you find the correct tempering of the 4ths, to complete the nine notes mini temperament. Nothing in this sequence is arbitrarilly set, but you have to find out the right amount of tempering of 3rds and 4ths within the octave.

It is already difficult to tune accurately A4 from an A4 fork, most procedures use F2 or B1 as a test note to accurately set the fundamental of A4 at exactly the same frequence of the fork.

But having A4 at 440 hz, when this note is not even tuned in your sequence seems to be impossible. In your sequence you tune all the notes from F3 to G4.

G#4 and A4 are not yet tuned, so I don't know from which note(s) you tune A4, maybe from A3, D4 and E4, anyway there are little chances that it falls exactly at 440 hz, it will depend mostly on the iH of the particular piano you are tuning.

By using a C5 fork, even the tuning of C4 is compromised!

So, in your sequence, not even a single note is accurately tuned to a given standard. The only thing you are sure is that 2nd partial of C4 is tuned at a C5 fork frequence, so the fundamental of C4, whatever it might be, will change from a piano to another due to differents amounts of iH.